翻訳と辞書 Words near each other ・ Equinox (celestial coordinates) ・ Equinox (comics) ・ Equinox (disambiguation) ・ Equinox (film) ・ Equinox (MLM) ・ Equinox (novel) ・ Equinox (Omar Rodríguez-López album) ・ Equinox (opera) ・ Equinox (OSGi) ・ Equianalgesic ・ Equiangular ・ Equiangular lines ・ Equiangular polygon ・ Equianharmonic ・ Equiano (crater) ・ Equiareal map ・ Equiaxed crystals ・ EQuibbly ・ Equibit ・ Equiceph ・ Equichordal point ・ Equichordal point problem ・ Equicizer ・ Equicom Savings Bank ・ Equiconsistency ・ Equicontinuity ・ Equidae ・ Equidiagonal quadrilateral ・ Equidigital number ・ Equidimensional Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Equiareal map ： ウィキペディア英語版 Equiareal map In differential geometry, an equiareal map is a smooth map from one surface to another that preserves the area of figures. If ''M'' and ''N'' are two surfaces in the Euclidean space R3, then an equi-areal map ''ƒ'' can be characterized by any of the following equivalent conditions: * The surface area of ''ƒ''(''U'') is equal to the area of ''U'' for every open set ''U'' on ''M''. * The pullback of the area element μ''N'' on ''N'' is equal to μ''M'', the area element on ''M''. * At each point ''p'' of ''M'', and tangent vectors ''v'' and ''w'' to ''M'' at ''p'', ::$|df\_p(v)\backslash times\; df\_p(w)|=|v\backslash times\; w|\backslash ,$ :where × denotes the Euclidean cross product of vectors and ''dƒ'' denotes the pushforward along ''ƒ''. An example of an equiareal map, due to Archimedes of Syracuse, is the projection from the unit sphere to the unit cylinder outward from their common axis. An explicit formula is :$f(x,y,z)\; =\; \backslash left(\backslash frac\{\backslash sqrt\{x^2+y^2\}\},\; z\backslash right)$ for (''x'',''y'',''z'') a point on the unit sphere. In the context of geographic maps, a map projection is called equiareal, area-preserving, or more commonly equi-area, if areas are preserved up to a constant factor; embedding the target map, usually considered a subset of R2, in the obvious way in R3, the requirement above then is weakened to: :$|df\_p(v)\backslash times\; df\_p(w)|=\backslash kappa|v\backslash times\; w|\backslash ,$ for some κ > 0 not depending on $v$ and $w$. For examples of such projections, see Equal-area map projections. Linear equi-areal maps are 2 × 2 real matrices making up the group SL(2,R) of special linear transformations. ==References== * Category:Functions and mappings 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Equiareal map」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.